Evaluating a double integral using Euler's method and Richardson extrapolation
Lietuvos Matematikos RinkinysWe transform a double integral into a second-order initial value problem, which we solve using Euler's method and Richardson extrapolation. For an example we consider, we achieve accuracy close to machine precision (~10-13).
Justin Steven Calder Prentice
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Geophysical Monograph Series, Page 263-304., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Jessica H. Whiteside +3 more
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On a vectorized version of a generalized Richardson extrapolation process [PDF]
Numerical Algorithms, 2016 Let $\{\xx_m\}$ be a vector sequence that satisfies $$ \xx_m\sim \sss+\sum^\infty_{i=1}α_i \gg_i(m)\quad\text{as $m\to\infty$},$$ $\sss$ being the limit or antilimit of $\{\xx_m\}$ and $\{\gg_i(m)\}^\infty_{i=1}$ being an asymptotic scale as $m\to\infty$, in the sense that $$\lim_{m\to\infty}\frac{\|\gg_{i+1}(m)\|}{\|\gg_{i}(m)\|}=0,\quad i=1,2,\ldots.$
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ERROR ANALYSIS OF RICHARDSON’S EXTRAPOLATIONS
International Journal of Computing, 2014 We propose estimators of a round off error contained in an approximation for Richardson’s extrapolation scheme under finite digit arithmetic. We also propose a stopping criterion, based on consideration of the round off error, for Richardson’s extrapolation scheme with respect to risk technical systems (automobile and railway transport, aircrafts ...
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Two Dimensional Richardson Extrapolation for Optical Waveguide Problems
, 1994 Integrated Photonics Research 1994, San Francisco, California United StatesLight propagation in optical waveguides is studied in the paraxial approximation using Richardson extrapolation.
Wai, P. K. A. +2 more
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Laser‐Assisted Phase Engineering of 2D MoS2 for Efficient Solution‐Processed Electronics
Advanced Materials, EarlyView.Here, local laser‐assisted phase transition from solution‐processed phase‐pure 1T′ to 2H MoS2 is shown to critically depend on the irradiation atmosphere. While processing in air leads to damaged insulating regions, inert conditions yield semiconducting 2H domains, enabling direct field‐effect transistor patterning with optimized lateral 1T′‐2H MoS2 ...
Anna Zhuravlova +10 more
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On the Effectiveness of Richardson Extrapolation in Machine Learning
CoRR, 2020 Richardson extrapolation is a classical technique from numerical analysis that can improve the approximation error of an estimation method by combining linearly several estimates obtained from different values of one of its hyperparameters, without the need to know in details the inner structure of the original estimation method.
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Linear multistep methods and global Richardson extrapolation
Applied Mathematics Letters, 2022 In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary differential equations numerically.
Imre Fekete, Lajos Lóczi
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Rethinking brachycephaly: Anatomical implications and health considerations in lagomorphs
The Anatomical Record, EarlyView.Abstract Brachycephaly in domestic rabbits is increasingly perceived by welfare organizations as associated with significant health complications, particularly oral pathologies. Despite this perception, comparative anatomical research into rabbit brachycephaly is limited compared to that of dogs and cats, compelling an in‐depth examination of its ...
Helaina Cressy +3 more
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Advances in Difference Equations, 2019 In this paper, the coupled space fractional Ginzburg–Landau equations are investigated numerically. A linearized semi-implicit difference scheme is proposed.
Yuan Xu, Jiali Zeng, Shuanggui Hu
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